The present invention relates to a brake system for motor vehicles which can be actuated in a brake-by-wire operating mode both by the vehicle driver and independently of the vehicle driver, and is preferably operated in the brake-by-wire operating mode and can be operated in a fallback operating mode without brake boosting, in which fallback operating mode only operation by the vehicle driver is possible. Such a brake system is known from international patent application WO 2004/080772 A1, which is incorporated by reference. The elastic element of the simulator device is embodied as a compression spring which is arranged in terms of its effect between the input force element and the restraining piston. Consequently, the restraining piston has to be held in the (normal) brake-by-wire operating mode against a stop which is fixed to the housing in order to make available a stable abutment to the aforementioned compression spring. When rapid activation of the pedal occurs in the previously known brake system, there is the problem that the electrically controllable pressure supply device, which is embodied as a motor pump assembly, cannot build up the necessary restraining pressure with the same dynamic so that a temporary movement of the restraining piston away from its stop can take place. This movement results in a brake pedal sensation which is unpleasant for the vehicle driver.